[tex]\it x\in(0,\ \dfrac{\pi}{2})\ \ \ \ \ \ \ (1)\\ \\ \\ cosx=tg(\dfrac{\pi}{3})sinx \Rightarrow \dfrac{cosx}{sinx}=\sqrt3 \Rightarrow ctgx=\sqrt3\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow x=\dfrac{\pi}{6};\ \ \ \ \ sin\dfrac{\pi}{6}=\dfrac{1}{2}[/tex]
